OSSOS: X. How to Use a Survey Simulator: Statistical Testing of Dynamical Models Against the Real Kuiper Belt Samantha Lawler, J. Kavelaars, Mike Alexandersen, Michele Bannister, Brett Gladman, Jean-Marc Petit, Cory Shankman To cite this version: Samantha Lawler, J. Kavelaars, Mike Alexandersen, Michele Bannister, Brett Gladman, et al.. OS- SOS: X. How to Use a Survey Simulator: Statistical Testing of Dynamical Models Against the Real Kuiper Belt. Frontiers in Astronomy and Space Sciences, Frontiers Media, 2018, 5, 10.3389/fs- pas.2018.00014. hal-02084080 HAL Id: hal-02084080 https://hal.archives-ouvertes.fr/hal-02084080 Submitted on 7 Jan 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution - NonCommercial| 4.0 International License METHODS published: 16 May 2018 doi: 10.3389/fspas.2018.00014 OSSOS: X. How to Use a Survey Simulator: Statistical Testing of Dynamical Models Against the Real Kuiper Belt Samantha M. Lawler 1*, J. J. Kavelaars 1,2, Mike Alexandersen 3, Michele T. Bannister 4, Brett Gladman 5, Jean-Marc Petit 6 and Cory Shankman 1,2† 1 NRC-Herzberg Astronomy and Astrophysics, National Research Council of Canada, Victoria, BC, Canada, 2 Department of Physics and Astronomy, University of Victoria, Victoria, BC, Canada, 3 Institute of Astronomy and Astrophysics, Academia Sinica, Taipei, Taiwan, 4 Astrophysics Research Centre, Queen’s University Belfast, Belfast, United Kingdom, 5 Department of Physics and Astronomy, The University of British Columbia, Vancouver, BC, Canada, 6 Institut UTINAM, UMR 6213 Centre National de la Recherche Scientifique-Université de Franche Comté, Besançon, France Edited by: Lorenzo Iorio, Ministry of Education, Universities and All surveys include observational biases, which makes it impossible to directly compare Research, Italy properties of discovered trans-Neptunian Objects (TNOs) with dynamical models. Reviewed by: However, by carefully keeping track of survey pointings on the sky, detection limits, J. Allyn Smith, Austin Peay State University, tracking fractions, and rate cuts, the biases from a survey can be modeled in Survey United States Simulator software. A Survey Simulator takes an intrinsic orbital model (from, for Akos Bazso, example, the output of a dynamical Kuiper belt emplacement simulation) and applies Universität Wien, Austria the survey biases, so that the biased simulated objects can be directly compared with *Correspondence: Samantha M. Lawler real discoveries. This methodology has been used with great success in the Outer Solar [email protected] System Origins Survey (OSSOS) and its predecessor surveys. In this chapter, we give †Present Address: four examples of ways to use the OSSOS Survey Simulator to gain knowledge about the Cory Shankman, true structure of the Kuiper Belt. We demonstrate how to statistically compare different City of Toronto, Toronto, ON, Canada dynamical model outputs with real TNO discoveries, how to quantify detection biases Specialty section: within a TNO population, how to measure intrinsic population sizes, and how to use This article was submitted to upper limits from non-detections. We hope this will provide a framework for dynamical Fundamental Astronomy, a section of the journal modelers to statistically test the validity of their models. Frontiers in Astronomy and Space Keywords: Kuiper belt, trans-Neptunian objects, observational surveys, survey biases, dynamical models, Sciences numerical methods, statistics Received: 31 January 2018 Accepted: 30 April 2018 Published: 16 May 2018 1. INTRODUCTION Citation: Lawler SM, Kavelaars JJ, The orbital structure, size frequency distribution, and total mass of the trans-Neptunian region of Alexandersen M, Bannister MT, the Solar System is an enigmatic puzzle. Fernandez (1980) described an expected distribution for Gladman B, Petit J-M and this region based on the mechanisms for the delivery of cometary material into the inner Solar Shankman C (2018) OSSOS: X. How System. Even before the first Kuiper belt object after Pluto was discovered, (1992 QB1; Jewitt and to Use a Survey Simulator: Statistical Testing of Dynamical Models Against Luu, 1993, 1995), it was theorized that dynamical effects produced by the mass contained in this the Real Kuiper Belt. region could in principle be detectable (Hamid et al., 1968). The first discoveries made it clear that Front. Astron. Space Sci. 5:14. extracting precise measurements of the orbital and mass distributions from this zone of the Solar doi: 10.3389/fspas.2018.00014 System would require careful analysis. Frontiers in Astronomy and Space Sciences | www.frontiersin.org 1 May 2018 | Volume 5 | Article 14 Lawler et al. OSSOS: X. How to Use a Survey Simulator Major puzzles in the Solar System’s history can be explored if as an alternate way to destroy the proto-Kuiper belt and capture one has accurate knowledge of the distribution of material in this many TNOs into resonances (Levison et al., 2008). In this model, zone. Examples include: the orbital evolution of Neptune (e.g., the giant planets undergo a dynamical instability that causes Malhotra, 1993), the large scale re-ordering of the Solar System Neptune to be chaotically scattered onto an eccentric orbit that (e.g., Thommes et al., 1999; Gomes et al., 2005), the process damps to its current near-circular orbit while scattering TNOs of planetesimal accretion (e.g., Stern, 1996; Davis and Farinella, and capturing some into its wide resonances (Tsiganis et al., 1997), the production of cometary size objects via collisional 2005). Due to the chaotic nature of this model, reproducing processes (e.g. Stern, 1995) and their delivery into the inner simulations is difficult and many variations on the Nice model Solar System (Duncan et al., 1988), and the stellar environment exist (e.g., Batygin et al., 2012; Nesvorný et al., 2013). One in which the Sun formed (e.g., Brunini and Fernandez, 1996; very recent and promising variation on the Nice model scenario Kobayashi and Ida, 2001). Our goal as observers is to test these includes the gravitational effects of fairly large (∼Pluto-sized) models and their consequences by comparison to the Solar bodies that cause Neptune’s migration to be “grainy,”having small System as we see it today. Given the sparse nature of the datasets discrete jumps as these larger bodies are scattered (Nesvorný and and the challenges of detecting and tracking trans-Neptunian Vokrouhlický, 2016). More dramatically, even larger planetary- objects (TNOs), a strong statistical framework is required if we scale objects could have transited and thus perturbed the young are to distinguish between these various models. Kuiper belt (Petit et al., 1999; Gladman and Chan, 2006; Lykawka The presence of large-scale biases in the detected sample and Mukai, 2008; Silsbee and Tremaine, 2018) of TNOs has been apparent since the initial discoveries in The level of detail that must be included in Neptune the Kuiper belt, and multiple approaches have been used to migration scenarios is increasing with the number of discovered account for these biases. Jewitt and Luu (1995) use Monte- TNOs with well-measured orbits; some recent examples of Carlo comparisons of Kuiper belt models to their detected literature comparisons between detailed dynamical models and sample to estimate the total size of the Kuiper belt, taking into TNO orbital distributions are summarized here. Batygin et al. account the flux limits of their survey. Similarly Irwin et al. (2011), Dawson and Murray-Clay (2012), and Morbidelli et al. (1995) estimate the flux limits of their searches and use these (2014) all use slightly different observational constraints to to weight their detections and, combining those with the results place limits on the exact eccentricity and migration distance reported in Jewitt and Luu (1995), provide an estimate of the of Neptune’s orbit in order to preserve the orbits of cold luminosity function of the region. Gladman et al. (1998) provide a classical TNOs as observed today. Lawler and Gladman (2013) Bayesian-based analysis of their detected sample, combined with test the observed distribution of Kozai Plutinos against the previously published surveys, to further refine the measurement output from a smooth Neptune migration model (Hahn and of the luminosity function of the Kuiper belt. Trujillo et al. (2001) Malhotra, 2005) and a Nice model simulation (Levison et al., determined the size, inclination, and radial distributions of the 2008), finding that neither model produces sufficiently high Kuiper belt by weighting the distribution of observed TNOs inclinations. Nesvorný (2015a) shows that the timescale of based on their detectability and the fraction of the orbits that Neptune’s migration phase must be fairly slow (&10 Myr) in were contained within the survey fields. Bernstein et al. (2004) order to replicate the observed TNO inclination distribution, and refined the maximum-likelihood approach when they extended Nesvorný (2015b) shows that including a “jump” in Neptune’s the measurement of the size distribution to smaller scales and semimajor axis evolution can create the “kernel” observed in the determined statistically significant evidence of a break in the cold classical TNOs (first discussed in Petit et al., 2011). Pike shape of the Kuiper belt luminosity function, later developed et al. (2017) compare the output of a Nice model simulation further by the deeper survey of Fraser and Kavelaars (2009). A (Brasser and Morbidelli, 2013) with scattering and resonant similar approach is taken in Adams (2010) who make estimates of TNOs, finding that the population ratios are consistent with the underlying sampling by inverting the observed distributions.